无标度网络的一个新的拓扑参数

为更深刻直观地定量刻划无标度网络的拓扑性质,将经济学中描述收入分配不均等程度的两个重要概念:洛伦茨曲线和基尼系数推广至一般的复杂网络.通过仿真和理论两个方面的工作,指出将这两个概念与幂律相结合可以更有效地刻划无标度网络的拓扑结构的异质性,同时还获得了关于无标度网络的一些重要性质.最后对基尼系数和网络结构熵进行了比较.

A New Topological Parameter of Scale-Free Network

To characterize scale-free network topology more intuitively and profoundly,Lorenz curve and Gini coefficient which describe income inequality in economics are generalized into complex networks where people in economics are corresponding to nodes in networks and income is corresponding to node degree.Through some fundamental simulations and mathematical analysis,it is found that by these two concepts one can characterize the heterogeneity of complex networks and can compare the heterogeneity of different complex networks,e.g.it is found that Internet is more heterogeneous than the star-shaped network of the same nodes.By evaluating Gini coefficients and dipicting Lorenz curves of 15 scale-free networks with their degree distribution exponents between 1 and 4,the reason why degree distribution exponents of most of real networks are located between 2 and 3 is explained.